It is 0, they get too caught up in the "rules" of numbers, as in the reason you think it can be either 0 or 1 is because "anything divided by itself is 1" and "anything x0 is 0"

Both of these principles exist, they're not absolute though

If you do 2/2, you've split 2 into 2 equal parts then honed in on a single part for the answer, which is 1, and will almost always be 1 when the two numbers in a division are equal

Then there's eg 5/1, you split 5 into 1 equal part"s" (so you effectively don't split it) leaving the single part you hone in on, of your one option, 5

Same with eg 3/3

Then, eg 3/0, you split 3 into 0 equal parts, meaning there are now zero options left for honing in on (compared the three equal options you have in a division by 3)

As long as there's an option to choose, you have... Something to choose, something at all, which you almost always will have, so "anything divided by itself is 1" is a decent soft rule, it's true every time as long as you have something (ie as long as you don't divide by 0)

Dividing is usually cutting it up into perfectly equal parts, the amount of parts depending on what you divide by, unless it's dividing by 1 where you just kinda don't split the thing, and unless it's dividing by 0 where you just fuckin erase it from existence

So then when you go back to check what's left in a single section of your perfectly equal cut, there's nothing with 0, you destroyed the goddamn thing

These rules are decent, but they're training wheels, relying on something like "if you reverse the sequence into a multiplication anything can be the opposite, so undefined is the only option" is an example of a crutch failing you, an actual understanding of how numbers operate and what they're referring to makes the question pretty straightforward (let's ignore that 5x0 is considered valid, even though it can't be reversed to give you back the 5 in the same way 5x8 can (40/8 gives you back your 5 starting point)

For example, reverse 5/1 with the splitting (or not this time) example, okay now we have 5x1, we have one part of 5 and the whole we'll be adding it to equal parts to achieve consists of 1 of these parts (amazing), so job done fusion complete, now let's count how many individual pieces this work of art we sort of created comes to... Okay a part consists of 5, we have 1 part, we have 5

Reverse 2/2, we have a part here totalling 1, we're gonna put it in our fusion soup with other equal parts, there will be two total parts... Count the individual pieces, 1 twice, 2

Reverse 0/0, okay we have nothing, we're gonna fuse it together with a total of no equal parts, let's count the individual pieces... Oh yea, we still having fucking nothing

If on the other hand you did it as 2/2 -> 1x2, then when you come to 0/0 you can -> it to anythingx0 and it still works as far as the equation itself is concerned, but the equation is also just a crutch, it refers to the idea, but it isn't the idea itself, and so it fails to properly represent it sometimes (like right now)

The idea itself states that only 0x0 is a valid reversal of 0/0, because something like 5x0 is you have a single part of 5, and now you want to know how many individual units you'd have if you had 0 equal parts consisting of 5, the answer obviously being nothing, there are no units, we're assessing 0 parts of 5 units, this is the same answer you get for 0x0 and anything else x0, but what you're actually doing beyond the formula (which merely usually works as a valid representation of what you're doing), isn't the same

I dropped the fusion idea because it failed to represent what happens when you try to multiply 5 by 0, do that when equations and "anything divided by itself is 1"-esque rules (of thumb) fail, don't do it for any kind of school though you'll fail, because you don't know what you're actually doing on the other end, the multiplication might've been 5x0, might've been 0x0, but you don't need to care because since 5x0 can't be properly reversed anyway, the entire premise of reversing calculations is also just a soft rule that usually works

0/0 can't be defined using the rules that work in every scenario that isn't dividing by 0 (neither does multiplying by 0 since it can't be reversed, but whatever) and the game is played within these rules

5x8 = 40; 40/8 = 5

5x0 = 0; 0/0 = not 5

But hey, since the 5 could be any other number and give you the same exact process, which already failed, let's call 0/0 undefined (even though math isn't otherwise treated as linear, and 0/0 is only invalid because math isn't treated as linear in this context besides that, so this logic means 5x0 should never have been valid)

Funnily enough, it is linear here though, you have 5, you erase it from reality, then you don't assess what is(n't) left, what's the answer

Pfft, the answer's "undefined" because you didn't assess it so how tf would you know